In a general univariate linear model, $M$-estimation of a subset of parameters is considered when the complementary subset is plausibly redundant. Along with the classical versions, both the preliminary test and shrinkage versions of the usual $M$-estimators are considered and, in the light of their asymptotic distributional risks, the relative asymptotic risk-efficiency results are studied in detail. Though the shrinkage $M$-estimators may dominate their classical versions, they do not, in general, dominate the preliminary test versions.
Publié le : 1987-12-14
Classification:
Asymptotic distributional risk,
asymptotic distributional risk efficiency,
James-Stein rule,
linear model,
local alternatives,
$M$-estimators,
minimaxity,
preliminary test,
robustness,
shrinkage estimator,
62C16,
62G05,
62F10,
62H12
@article{1176350611,
author = {Sen, Pranab Kumar and Saleh, A. K. M. Ehsanes},
title = {On Preliminary Test and Shrinkage $M$-Estimation in Linear Models},
journal = {Ann. Statist.},
volume = {15},
number = {1},
year = {1987},
pages = { 1580-1592},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350611}
}
Sen, Pranab Kumar; Saleh, A. K. M. Ehsanes. On Preliminary Test and Shrinkage $M$-Estimation in Linear Models. Ann. Statist., Tome 15 (1987) no. 1, pp. 1580-1592. http://gdmltest.u-ga.fr/item/1176350611/